"Freeze out" match strategy
Dbroth02
I was recently introduced to the idea of a "freeze out" match, and am curious
about appropriate match strategy.
For those unfamiliar (as I was) with the rules for a "freeze out" match, I will
reproduce the rules that I saw posted for a side event in the Michigan Summer
Backgammon Championships, directed by Carol Joy Cole:
<START rules>
1. All matches will be played to a 5 point differential. That is, a winner is
declared when s/he is 5 or more points ahead of his/her opponent. Examples:
If a player has just won a game making the score 8 to 3, then s/he has won the
match and will advance to the next run. If a player wins a game and the score
is 7 to 3, then another game must be played, until one player has achieved a 5
or more point lead over his/her opponent.
2. Doubling cube. The cube will start at "One" for the first five games. The
cube will start at "2" for the second five games. The cube will start at "4"
for the third five games. If need be, the cube will start at "8" the next five
games.
3. Standard tournament rules apply except the Crawford, Holland and Jacoby
rules are NOT in affect.
This event is designed to provide a new challenge to tournament style play.
All participants are encouraged to relax and enjoy this format and to exercise
patience if any idiosyncrasies or problems arise as a result of this format.
Thank you and good luck.
<END rules>
I'm relatively new to the world of regular backgammon match strategy, but have
a math/stat background. After reading Woolsey's "How to play Tournament
Backgammon", I can grasp the general ideas behind equity tables and their usage
in a regular backgammon match. Some of the same ideas must apply to the
"freeze out" format, but clearly many of the particulars would change.
In general, it seems that the longer a "freeze out" match lasts, the less
important having a lead becomes - the cube escalation feature certainly gives
the trailer more than the usual chances to come back. In fact, match equity
seems to be a function of what game it is as well as the score.
For a simple example of this, your match equity (under the usual assumptions)
for the 16th game of the described "freeze out" match (the first one where the
cube is on "8") would be 50% at ANY match score. If either player trailed by 4
points, then they would double to "16" at the first opportunity (no Crawford
rule), so the match will go to the winner of this game. If the match is
closer, the match will go to the winner of this game without the cube being
turned.
I don't know what your match equity (under the usual assumptions) is with a 4
point lead entering game 2 of the described "freeze out" match. It is clearly
larger that 50%, and I conjecture that a 4 point lead would be less valuable in
each subsequent game, with relatively small drops between games when the cube
doesn't escalate, and relatively large drops when it does (entering the 6th,
11th, and 16th games).
I further conjecture that the match equity with a 4 point lead entering game 2
of the described "freeze out" match is less that of a (-5,-1) Crawford game in
a regular match (85% in Woolsey's table) and also less than that of a (-5, -1)
post Crawford game in a regular match (Woolsey gives no post Crawford match
equities, presumably since there are no post-Crawford decisions based on them,
but it would have to be at least a couple percent less than the same score
during the Crawford game, with no free drop available to the leader, so say 83%
as an upper bound?).
Perhaps those with experience in "freeze out" matches can provide some further
insight into appropriate strategy (and/or amusing war stories!).
Dave Brotherton